All About Angles and Axes of the Eye: Visual Axis, Optical Axis, Pupillary Axis, Angle Kappa, and More.
‘Axes of the eye’ is the most conflicting topic in the ophthalmic world. Varieties of axes and angles of the eye have been defined over the years. Some of the definitions and explanations are practical, while others exist only in theory.
According to Oliver Findl MD (Austria), there is some confusion of terminology and also many of the terms have been used interchangeably. To be honest most of us are not really quite clear about the angle and axes of the eye.
Some of the nomenclatures of axes and angles are still disputed in medical science. We will try to present a clear picture of the angles and axes of the eye in today’s topic.
Axes of the Eye
Two popular axes of the eye are the optical axis and the visual axis. In literature, the visual axis and the optical axis are also referred to as the line of sight and the pupillary axis, respectively. Both of these are imaginary lines.
The visual axis is one of the eye’s many axes. Other axes of the eye include the optical axis, the pupillary axis, the line of sight, and the fixation axis. Some of the definitions, however, are used purely in a theoretical sense than they are in a clinical setting.
Optical Axis of the Eye Or Optical Axes of the Eye
The imaginary line which is perpendicular to the cornea and that intersects the center of the entrance pupil is known as the optical axis of the eye. The optical axis is also defined as the theoretical line which passes through the center of all refractive media of the eye.
The optical axis actually doesn’t intersect with the retina at the center of the fovea as might be expected. The line intersects the retina slightly towards the nasal side from the fovea, so that there is an angle of about 5 degrees between the visual axis and the optical axis.
The optical axis passes through the center of the cornea as well as the center of all the elements of the eyeball, i.e. the center of curvature of two surfaces of the cornea, the center of curvature of two surfaces of the crystalline lens, and the nodal point of the eyeball.
If the optical surfaces of the eye were perfectly coaxial, the reflected images from each optical surface would appear aligned from the perspective of an object that is positioned on the optical axis. The Purkinje images (I, II, III, and IV) are the reflections of objects from the structures of the eye, namely the outer corneal surface (I), inner corneal surface (II), anterior surface of the lens (III), and the posterior surface of the lens (IV) respectively. These images are however seldom observed to be coaxial showing deviations from an ideal coaxial optical system.
It is easy to understand the optical axis in an optical system. It is the line going through the center of the curvature of all the refractive surfaces. But, in the human eye, an asymmetrical optical system, the surfaces of the cornea and the crystalline lens are not actually aligned. Some degree of tilt and some distance of decentration occur. Therefore, the eye doesn’t really have an optical axis, Dr. Artal mentioned.
The optical axis is only a theoretical concept that applies best to eye models and schematic eyes where the refractive surfaces are centered with respect to one another.
Optical Axis in Lens and Mirror
In a lens, the optical axis is defined as the straight line that passes through the geometrical center of a lens and joins the two centers of curvature of its surfaces. Sometimes, it is also known as the principal axis.
The path of a light ray along this axis is perpendicular to the surfaces and, as such, will be unchanged. All other ray paths passing through a lens and its optical center (the geometrical center of a thin lens) are called secondary axes.
The optical axis of a curved mirror passes through its geometric center and its center of curvature.
NOTE: The term optical axis should not be confused with the optic axis, a term used in crystallography.
Visual Axis of the Eye Or Visual Axes of the Eye
The visual axis is one of the most discussed axes of the eye. The imaginary line which connects the fixated object in space, the center of the entrance and exit pupil, and the center of the fovea is known as the visual axis of the eye. It is also known as the foveal-fixation axis. It can also be defined as the line joining the fixation point, nodal points (N and N’), and the fovea.
The visual axis can be defined as the nodal ray that strikes the foveola with zero transverse chromatic aberration (TCA). Therefore, the visual axis is also called the foveal achromatic axis.
The visual axis does not necessarily pass through the pupil center and can be imagined as a straight line from the fixation point to foveola (with the patient fixating), representing an undeviated or minimally deviated ray of light.
Pupillary Axis of the Eye Or Pupillary Axes of the Eye
The pupillary axis of the eye is a line perpendicular to the cornea that passes through the center of the entrance pupil and the center of curvature of the anterior corneal surface.
The pupillary axis with relation to a natural undilated pupil should be used to gauge IOL (intraocular lens) centration, tilt, and in the case of toric IOL’s rotation because that is how the best visual results can be obtained.
The pupil center can be observed directly. The pupillary axis can be determined by locating a source such that the reflected image of this source (when viewed from the source) is centered on the entrance pupil.
Fixation Axis of the Eye Or Fixation Axes of the Eye
The fixation axis is the line joining the fixation point and the center of rotation of the eyeball.
The line of sight (Axes of the Eye)
The line of sight of the eye is the ray from the fixation point reaching the foveola through the pupil center. The line of sight (LOS) is slightly different in the object and image plane of the eye. In general, it can be imagined as a broken line representing a deviated ray of light, going from the fixation point to the PC (with the patient fixating) and eventually reaching the foveola after refraction at each optical interface.
The LOS is associated with a comparatively longer optical path difference (OPD) compared to the visual axis, also showing transverse chromatic aberration, unlike the visual axis. It can be determined using 2 different point sources at different distances from the eye fixated simultaneously, one focused on the retina and one out-of-focus.
If the chief rays from both sources are coincident and they lie on the LOS, the ray from the out-of-focus source shall form a blur circle while the ray through PC (focused source) shall form the center of the blur circle.
Angles of the Eye
Angle alpha is defined as the angle formed between the optical axis and the visual axis of the eye.
Angle gamma is defined as the angle formed between the optical axis and the fixation axis.
Angle kappa is formed between the pupillary axis and the visual axis measured on the center of the pupil from outside the eyeball.
Angle lamda is formed between the pupillary axis and the line of sight. However, because the line of sight is nearly identical to the visual axis, and because the eye’s nodal point cannot be determined with current technology, angle lambda tends to be referred to clinically as angle kappa.
In practice, the values of kappa and lambda angles are very close: remember that the distance between the respective corneal intercepts of the line of sight and the visual axis is (despite clinical relevance) short (a few hundredths of a millimeter compared to the distance between these points and the corneal intercept of the pupil center.
Importance of visual angles Kappa and Lamda in axes of the eye
The visual angles lambda (λ) and kappa (κ) are clinically important when it comes to the surgical centralization of the cornea in the LASER refractive surgery, but they are not considered for multifocal intraocular lens (IOL) implantation.
The angles λ and k are positioned in the nasal direction to the pupil, decreasing as the individual grows, being on average 8.3° at birth and around 5,0° in adult life.
According to Abrahao RL et al., there was a correlation between the presence of a larger angle lambda and the smaller axial lengths for both eyes. For the hypermetropic spherical equivalent, there was a correlation with the presence of a larger angle lambda only for the left eye.
Their study suggests partiality in multifocal IOL implants in the presence of a significant angle lambda based on the theory that the presence of said angle regulates the balance between the aberrations of the corneal surface versus the crystalline.
Clinical Implications of angles and axes of the eye
Hyperopic LASIK Refractive Surgery
The area of laser focus greatly determines the refractive surgery outcomes. Studies have compared the outcomes in LASIK surgery when focusing on:
1) the center of the pupil,
2) the corneal light reflex,
3) the corneal vertex, and
4) halfway between the center of the pupil and the corneal light reflex in patients with a large angle kappa.
A systematic review of these studies revealed that, in patients with significant hyperopia, centering on the corneal light reflex results in better corrected and uncorrected visual acuity, less decentration of the ablation zone, and less higher-order aberrations.
The same conclusions cannot be made for mild hyperopes with smaller angle kappas, so for these patients, it may be equally safe and efficacious to center over the pupil.
Myopic LASIK Refractive Surgery
Angle kappa is also a significant factor when performing myopic LASIK refractive surgery. According to Okamoto et al, approximately one-third of myopic LASIK candidates have an angle kappa large enough to warrant centering closer to the visual axis.
Additionally, Arbelaez et al compared the outcomes in LASIK centered over the pupil to LASIK centered over the corneal vertex in 52 myopic patients with a moderate to large angle kappa.
Presbyopic Corneal Inlays
For optimal presbyopic correction, the centration of corneal inlay plays a vital role. In patients with a significantly large angle kappa, the center of the inlay – identified by the coaxially sighted corneal light reflex – should be placed halfway between the corneal vertex and the center of the entrance pupil.
Small Incision Lenticule Extraction (SMILE)
SMILE does not involve cutting a flap in the cornea like LASIK. The adjustment of the intraoperative angle kappa during the SMILE procedure was found to result in fewer higher-order aberrations.
It is useful to consider angle kappa while using multifocal IOL in cataract surgery, especially for hyperopic patients with a large angle kappa. Studies have shown that eyes with a larger angle kappa are correlated with more glare and more halos after cataract surgery with placement of multifocal IOLs.
It occurs due to decentration. Here, the light rays miss the central optic zone and pass through a multifocal ring, resulting in glare and halos.
In pediatric patients, the corneal light reflex and red reflex are the basis of the Hirschberg and Bruckner tests which are used to assess for strabismus, a condition in which the optical axes are not aligned.
Because the fovea is one of the terminal points of the visual axis, any pathology that disrupts the foveal anatomic location can lead to alterations to this axis. In entities such as choroidal neovascularization from age-related macular degeneration (AMD), the contour and location of the fovea are altered.
Altered optical axes of the eye are more commonly seen in pathologies causing drag of the fovea such as in retinopathy of prematurity or familial exudative vitreoretinopathy.
- Artal, P. Optics of the eye and its impact on vision: a tutorial. Advances in Optics and Photonics, 2014;6:340–67.
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